A357013 - OEIS

%I #7 Sep 25 2022 11:05:17

%S 1,2,1,12,4,2,120,30,12,6,1680,336,112,48,24,30240,5040,1440,540,240,

%T 120,665280,95040,23760,7920,3168,1440,720,17297280,2162160,480480,

%U 144144,52416,21840,10080,5040,518918400,57657600,11531520,3144960,1048320,403200,172800,80640,40320

%N Triangle read by rows. T(n, k) = ((2*n)! * k!) / (n + k)!.

%e [0]        1;

%e [1]        2,       1;

%e [2]       12,       4,      2;

%e [3]      120,      30,     12,      6;

%e [4]     1680,     336,    112,     48,    24;

%e [5]    30240,    5040,   1440,    540,   240,   120;

%e [6]   665280,   95040,  23760,   7920,  3168,  1440,   720;

%e [7] 17297280, 2162160, 480480, 144144, 52416, 21840, 10080, 5040;

%p T := (n, k) -> ((2*n)! * k!) / (n + k)!:

%p for n from 0 to 6 do seq(T(n, k), k = 0..n) od;

%Y Cf. A001813 (column 0), A000142 (main diagonal).

%K nonn,tabl

%O 0,2

%A _Peter Luschny_, Sep 25 2022